Let $A$ be a $k\times n, k<n-1$ random matrix with entries drawn i.i.d. from a standard Gaussian, and $B$ a $k\times m$ random matrix with entries drawn i.i.d from a standard Gaussian, and independently of the entries of $A$.
Is there any upper bound known about the largest singular value of this matrix: $(BB^T)^{-1/2}A$?